I am sorry to learn of this situation, and dealing with debt collection matters (particularly when you are also dealing with medical issues) is a difficult matter.
Unfortunately the debt collector still has a contractual right to pursue you for collections (so long as their conduct is within the bounds of the Fair Debt Collections Act: https://www.consumer.ftc.gov/articles/0149-debt-collection).
As far as bargaining power, most debtors that have more debts than they can afford to pay have the backdrop of filing bankruptcy (so if the creditor pushes too hard, they will be left with nothing to collect against - once the debtor files for bankruptcy they are going to be unable to pursue the matter further as the bankruptcy discharge will make the claim unenforceable).
When trying to settle a debt, creditors generally prefer lump sums over payment plans. They are often willing to accept an amount less than the full debt (the trade off is that they get a quick payment and don't have to worry about ongoing collection costs or administration). If you do not have the ability to offer a lump sum for something the creditor will accept (some will accept a small portion, while others want close to the full amount), you can try a payment plan, these are less satisfactory to the creditor (especially if they have a lien on your property already), but if you are willing to offer something with a reasonable chance to get the creditor a large amount of their debt back, you are likely to get them to accept it.
Whenever working with a creditor, make sure that you keep your communications in writing (if you speak to someone by phone, promptly send a confirmation letter to summarize your conversation), as this will help to ensure that there is no confusion later on, and you will be able to enforce your settlement against any future collection efforts.